Determination of dynamic unbalance



April 18, 1961 w. M. GRUBER ETAL 2,980,331

DETERMINATION oF DYNAMIC UNBALANCE 3 Sheets-Sheet 1 Nrw? GRI/BEK WAK/IEN M. fxN/WD 7T Sv/HEL Wim Avvmwm April 18, 1961 w. M. GRUBER ETAL 2,980,331

DETERMINATION OF DYNAMIC UNBALANCE Filed May s, 1956 s sheets-sheet 2 XII-Pfff. Cf# f j l|| l' I," K rluP/X i M" "711| M 4 l 6/ 56 .73| l I I Z4 'a h April 18, 1961 w. M. GRUBER ET AL 2,980,331

DETERMINATION oF DYNAMIC UNBALANCE 3 Sheets-Sheet 3 Filed May 3, 1956 United States Patent F DETERMINATION OF DYNAMIC UNBALAYCE Warren M. Gruber, Horsham, and Bernard T. Svihel,

Croyden, Pa., assignors to Tinius Olsen Testing Ma- `chine Company, Willow Grove, Pa., a corporation of This invention relates to the determination of dynamic unbalance in rotatable articles. Y

Dynamic unbalance in a rotating body is due to the force couple set up by the unbalanced distribution of weight and is usually evidenced by the vibration of the body on its supporting bearings. Correction is ordinarily alorded by nding the amount and location of unbalance in two correction planes spaced from one another along the rotational axis of the body and then adding or removing weight so, in effect, to form a couple equal and opposite to that causing the original unbalance.

In determining unbalance, an article is rotatably mounted in a balancing machine cradle arranged on elastic supports so as to have a single degree of freedom of motion in each of the correction planes. The unbalance causes the cradle and article to vibrate, and the amount and location of unbalance in each correction plane is measured. In determining the unbalance in one correction plane, it is, of course, necessary that the effect of unbalance in the other plane be compensated for or be eliminated. This is usually done by providing pivots for the correction planes so that the cradle can vibrate only in one correction plane at a time.

Most articles whose dynamic unbalance is to be determined permit pivotal supporting as mentioned above. However, in many instances, the shape of the article is such that it is impractical to provide pivots in the planes of correction so that it is impossible, from a pivoting standpoint, to eliminate the elects of unbalance in one plane while the unbalance in the other is being measured. The present invention provides apparatus for the determination of unbalance Vin articles of the type last men- Patented Apr. 1s, 1961 automatically determining unbalance as disclosed in cci--A pending application of John Reed Stovall, Jr. and Irving Weintraub, Serial No. 233,294, filed June 25, 1951, now

Patent No. 2,783,648; While other systems or apparatus for determining unbalance may be used in connection with the present invention, the apparatus disclosed in said application is preferred. On'the base 1 are mounted pedestals 3 and 4, which are axially adjustable to accommodate articles of different lengths. Mounted at opposite ends of each pedestal are pairs of elastic rods or supports, one pair for pedestal 3 being indicated by the numeral 6 and a similar pairfor pedestal 4 being indicated by the numeral 10. On the top of each pair of rods are cross supports 11 and 12 secured thereto. by clamps, for example, the clamps 13-13 for the rods 10 as shown in Figure 3. Each pair of rods is provided with'tuning means, for example, the clamps 14 and 15V which arc slidably adjustable on the pedestals 3 and 4. f

On the top of each pedestal is mounteda pair of lock-A ing pins, the locking pins 16-16 on top of the pedestal 4 being best seen in Figure 3. One of the locking pins 17 on the pedestal 3 is indicated in Figure 2. The lockf ing pins are controlled by hydraulic or electric mechanism (not shown) so as to be disposed in-apertures in the cross brackets, for example, the apertures 21-21 for the locking pins 16-16, or alternatively, the Vlocking pins may be withdra-wn from the apertures. When withdrawn, the cross member is freeto vibrate on the elastic rods, for example, the cross member 12 can move `from left to right as viewed in Figure 3. When the locking pins are within the apertures, the cross member isheld fixed.

The cross member mounts swivel supports 23 and` 24 for an article to be tested, and since both Vare identical, only the details for the support in the cross member 12 will be described. The pedestal 4 is provided with a cen tr-al recess 25, which accommodates a downwardly ex'- tending portion 26 of the cross member 12. A pair of roller bearings 27-27 is mounted in the cross member and supports a vertically extending shaft 28. v On the top of the shaft 2S is arranged a yoke29, It will be apparent thatthe bearing arrangement permits the shaft and yoke to swivel in a horizontal plane relative tothe cross memprovided in planes other than the correction planes,

measuring the unbalance preferably in these other planes (hereinafter called measurement planes) and then feeding te unbalance information to a device which computes the unbalance in the correction plane so that weight can be added or removed.

The manner in which the foregoing is accomplished will be apparent from the following description and drawings wherein: Y

Figures la and lb are diagrammatic representations of articles supported other than in correction planes and illustrating in particular certain unbalance moments;

Figure 2 is a side elevational view illustrating a balancing machine, the cradle of which is pivoted in planes other than in the correction planes of the article;

Figure 3 is a fragmentary view of certain of the parts of Figure 2;

Figure 4 is a circuit diagram illustrating one embodimentof apparatus for computing the unbalance in the correction planes; and

`Figure 5 is a circuit diagram illustrating another embodiment of apparatus for computing the unbalance in the correction planes.

ln Figure 2 the balancing machine comprises a base 1 supporting a housing 2, which encloses apparatus for ber. On the bottom of the portion 26 are-disposed two paddles 31-31 which extend downwardly into a reservoir of oil (not shown) in the pedestal. The paddles and oil provide for the dampening of the vibration vof the cross member 12. The yoke 29 carries a pair of roller bearings 32 and 33 which support the shafts V34 and 35 of a lower frame 36. The frame 36 carries a bush-type bearing 40.

The shaft 41 of an article to be tested is disposed in the bushing 40. An upper frame 42 having a bush-type bearing 43 surrounds the top half of the shaft and is secured to the lower frame by the screws i4-44. The bushing provides for the shaft to be rotatable therein. As best seen in Figure 2, the yoke 46 of the support 2 4 carries a bracket 50 mounting a beam 51. carrying at its end an axially adjustable upright bearing 52. This bearing carries a drive shaft 53 which is. connected by universal joints 54 and 55 to driving mechanism (not shown) within the housing 2. On the end of the shaft 53 is aecoupling 56 having a plurality of drive pins 60 which are adapted to be inserted in apertures'l in an adaptor 62 adapted to be fixed to the shaft 41.

Located in each of the transverse planes containing the swiveling axes of the supports are unbalancesignal pickups preferably ofthe permanent magnet moving coil type, the magnet being supported on an upright and the coil'being secured to a rod attached to a cross member. For example, as seen in Figure 3, the magnet for pickup 63 for the left-hand plane is mounted on pedestal 64 and the coil which operates within the magnet is se.- gured toa rod 65 mounted on cross member 12. i Y

i correction planes, vand d theV l ment planes;

f It will be apparent'from the above description thatv Y 1 if Vthevarticle to be tested isjrotated, and say, the righthand support 251 is free (by the locking pins `being withdrwn and the left-hand ,support z3 is maken i1-notV ficeto vihrt-lbyits locking'vpins beinginseited), un? balance'willfcause the cross member 1I Yand VVarticletol vibrate Vin a horizontal plane, the motion being accom.

l24, In 'either instance,Y of course, Ythe universal joints 54Y and 55 Ypermit the reguiredvrnovement of the drive i 635 ana .the svi-wei and is indicated by the dotted line M1. The pick-up and Vthe swivel axis of the support'24 lie in the right measure-A -Y ment plane MrlAWhenV the support 23 is free to vibrate, the unbalancersignal inthe Mi plane is developed by the 'pick-ppo land` when the support 24Y is free torvibrate,

' theyunba'lancesignal'for the.Mr plane is developed by t'hefother pick-up. v Y f In Figure 2,we have diagrammatically illustrated two types. of articles `which are ofV a nature so as to he l10n#V supportable at the pivots when correction is to be made.V

For example, the article X, which may beta turbine i blade assembly, is arranged for testing inboard VVf the supports 23 and 24.Y The article Y, which may be a fan,`

' by' theexing of rodsultlandl the swiv'eling of support Y axes/ofthe supports lie inY the same transverse plane'. Y This Yplaneris calledherein'rthe vleft measurement plane is-arranged outboard of the supports 23 and 24. The

' le'ftandl right correction planes for both articles are Vdesignated by-C1 andCp 1 For either type article,V the unbalance r(angleV Vand l amount) in Vboth measurementplanes Vis first `measured andthen the unbalance inthe correction planes yis deter- Y mined or computed. The material which follows briefly describes the equationsinvolved inthis computation.

In Figure la Ywith the support 23` locked and suPPQrt ngleindicated at 80. With the vsupportY 24 locked and Y`the-sirlpport 23a-free, the article -will vibrate about 24 through the angle 81'; YYIt will be observed that in either .'ins'tance'the article is vibrating in both the right andV lefti correction planes and inV thej corresponding? measurement Y' plane; YThe unbalance inthe lefttcorrection plane-can Y he` Yrepresented `by vector KLa, in the rightcorrection Y plane by vector. L, and the unbalance measured in they measurementplanes can'be ,representedrby vectors A09 and B. K, L, A andB are quantities represent- .ingV magnitudes of unbalance and ltheir-corresponding angles a, 07, and kp locate the respective vectors from 1x-common referenceplane, for example, a horizontal planeV when 'the article is in a predetermined rotational position. Itv might `be'pointed out that the term horif zontal refers to aV reference plane and, therefore, is used inthe"genericfsense, i.e., Ythereference point or plane may beY horizontal or verticalor in'some intermediate f position. Indeed,"if therotational'axis of the part'to be Y testedv is disposed in aY vertical position, the` reference planefwill be correspondingly arranged. In thegure, c representsf the distance between correction .iplane`s, d and b the distances between respectiveV measurement and distance betweenY measureztan 11g/K1. Also, K1=K cos a and` Kga-K sin a. Similar equations can be written for L, A and B and their corresponding angles a, 0 and qb. vThe solution for Equations l and 2 can be shown to be: (3. n e @www YV' r-Bpbizff'hll Y Y .Y d

(3) Ll: 'V-'Aia-i-cBrbd Bil:

= B2b-'Azurite The Equations 3a, etc., Aq, etc., areY termed` hereinafter operating equations; -Where the article is mounted outboard ofthe measurement plane, a similar analysis applies in determining the'operating equations. In Figi ure 1b the article TY is mountedroutboardrof the sup- ,ze free, me article x .win vibrate abatir zsuirouggh the' (6) 2M24=0=Kw+l ,my Y

ports 23 and24and the samesymbols as in :Figure la are used to designate the correction planes, etc. Y WithsiupportZflfree, Q g' Y L2=Aaigb B C Y With the aboveV equations in"`mind,litY is pointed out that the amount and angle of unbalance in each of the Y Ycorrection planes (for eitherrtype of article) 'is found by determining the amount and angleoiunbalance in Veach of the measurement planes and 'resolving the vectors vrepresenting'the sameinto 'horizontal and vertical VV'corn- 1 piments, performing the computation. required by'thc Y"K a=K1+iKfwhere Klrand K2Y areY ,the 90- or horizontal and lvertical 4components jof'funbalance. `Also,

particular operating equations Vselectedrto, find `the horizontal and vertical components in Ythecorrection plane l Yand then resolving these latter componentsjintoresulting vectors. The value andV angle of each Vresulting Yvector f Yrepresents the magnitude and angle of'unbalance in the ,i respective correction planes.

The materialV which follows describespan embodiment for performing the above'4 andsadapted particularly for :operating Equations k31.,'3,b", 3V 'and 3d. l

In the embodiment shown in Figure A,V a regulated power supply is generallyzdesignated by the `letter P. This has-a commercial Vll'fvolt, ofcycleinputilll),'B+

output 101, filament supply 162 and output lines 103. The output feeds lines 104 to supply a constant A C. voltage to a servo motor which will be described later. 'I'he output lines supply a transformer 105, the secondaries 110 and 111 of which respectively supply constant A.C. voltage to the potentiometers 112 and 113.

The potentiometers are adapted to develop voltages respectively representing the magnitude of unbalance in the left and right measurement planes. The movable arm 114 of the potentiometer 112 is adapted to be adjusted in accordance with the amount of unbalance in the left measurement plane, while the movable arm 115 of the potentiometer 113 is adapted to be moved in accordance with the amount of unbalance in the right measurement plane. Thus, the output voltages of the potentiometers are in terms of volts per unit of variable, or represent or are proportional to the amount of unbalance in the respective measurement planes. The output voltages are labelled A and B.

The voltages A and B are fed to devices which develop voltages proportional to the respective horizontal and vertical components thereof. Preferably these devices take the form of non-linear potentiometers which operate to multiply the inputs thereto (A and B) by the sine and cosine of the respective angle of unbalance and thereby obtain the horizontal and vertical components. The voltage A is fed to the left potentiometers generally designated by 117 and 118, while the voltage B is fed to the right potentiometers generally designated by 119 and 120. The left and right potentiometers are arranged substantially identically, and the detailed description which follows covers the left potentiometers 117 and 118.

The potentiometer 117 has an annularly-arranged resistance 121 and the ganged arms 123 and 124, which are angularly spaced 90 from one another, are adapted to be rotated about the resistor. The potentiometer 118 has an annularly-arranged resistor 122 and the ganged arms 125 and 126, which are spaced 90 from one another, are adapted to be rotated about the resistor. The resistor 121 is center-tapped to ground as indicated at 129 and 130 and the input voltage A is symmetrically connected between tapsas indicated at 131 and 132. The resistor 122 is also center-tapped as indicated at 133 and 134 and the input voltage A is symmetrically connected between taps as indicated at 131' and 132'.

The arms 123- 124 and 125-126 are preferably ganged so as to be movable in unison about the respective resistors and are adapted to be moved in accordance with the angle ofvunbalance 6 in the left measurement plane. In the position shown, the arms are set for an angle of 0 and when the arm 123 is at tap 130, it represents an angle of 90. The voltage A1 appearing on the arm 123 will be a function of the cosine of 6 or A1=A cos H, while the voltage A2 appearing on arm 124 will be a function of the sine of 0 or A2=A sin '6. As has been indicated hereinbefore, A1 and A2 represent the horizontal and vertical components of unbalance in the left measurement plane.

With reference to the Equations 3a, etc., 4a, etc., and 7a, etc., mentioned above, it will be noted that these require horizontal and vertical components of both positive and negative sign. Except as noted hereinafter, the negative voltages are provided by the potentiometer 118, since the voltage appearing on arm 125 is the same as, but displaced 180 from, the voltage of the arm 123, while the voltage on the arm 126 is the same as, but displaced 180 from, the voltage on the arm 124. These voltages on the arms 125 and 126 are respectively indicated as A1 and -A2. The leads 140, 141, 142 and 143 from the potentiometers are indicated as having voltages +A1, A1, |A2 and A2.

The voltage B is fed to the potentiometers 119 and 120, which are arranged similarly as the potentiometers V117 and 118, but actuated in accordance with the angle e Ain the right measurement plane, and the leads '144, 145,

146 and 147 are indicated as having voltages B1, {B1,r B2 and |B2 respectively representing the horizontal and vertical components of imbalance in the right measurement plane.

The horizontal and vertical voltages for the potentiometer are fed to transfer switches generally designated by 150 and 151. These switches operate to condition the system alternatively for operation when articles such as X or Y are being tested. The details of construction follow.

Switch 150 has upper portion 150u and lower portion 1501 and switch 151 has upper portion 15114 and lower portion 1511. In the upper portion 1501: of the switch 150, the two top terminals are interconnected to the line having the voltage +A1. The bottom terminals are'interconnected to the line 141 carrying Vthe voltage A1 and also interconnected to a resistor 152i. The left-hand movable arm of the switch in'interconnected to a resistor 154, while the right-hand movable arm of the switch is interconnected vto a potentiometer 155. In the lower portion 1501, the two top terminals are interconnected to the line 142 carrying the voltage |A2, while the lower terminals are interconnected to the line 143 carrying the voltage A2 and also interconnected to a resistor.156. The left-hand movable arm is inter-` connected to a resistor 160 and the right-hand movable arm is interconnected to a potentiometer 161.

In the upper portion 151u of the switch 151, the two top terminals are interconnected to the line 144 carrying the voltage B1. The lower terminals are interconnected to the line 145 carrying the voltage -l-B1` and also interconnected to a resistor 162. The left-hand movable arm is interconnected to a resistor 163 and the right-hand movable arm is interconnected to a potentiometer 164. In the lower half 1511, the two top terminals are interconnected to the line 146 carrying the voltage B2. The lower terminals are interconnected to the line 147 carrying the voltage -|-B2 and also to a resistor 165. The left-hand movable arm is interconnected to a resistor 166, while the right-hand movable arm isinterconnected to'a potentiometer 170. The position of the movable arms of the switches 150 and 151 shown in full lines conditions the syste'm for operation when an article such as X isV being tested, and Vwhen the arms are in the position shown by the dotted lines, the system is conditioned for operation when an article such as Y is being tested. rl`he switches are ganged fo simultaneous operation as is indicated.

With the right-hand movable arms of the switches 15 and 151 positioned as shown, it will be apparent that the voltage A1 appears across the potentiometer 155, the voltage A2 appears across the potentiometer 161, the voltage B1 appears across the Vpotentiometer 164, and the voltage B2 appears across the potentiometer 170. These potentiometers are multipliers and perform the multiplying operations in accordance with the operating equations, i.e., respectively operate to multiply the horizontal and vertical components of the measurement planes by their distances Vto the correction planes.

Thus, the resistances of the potentiometers 155 and 161 are arranged so that the movable arms 171 and 172 can be set thereon in accordance with the distance a between the left measurement and left correction planes. Therefore, the voltage appearing on the arm 171 is -l-A1a and the voltage on arm 172 is +A2a. As indicated, these arms are arranged for simultaneous movement. The resistances of the potentiometers 164 and are arranged so that the movable arms 173 and 174 can be set thereon in accordance with the distance b between the right measurement plane and the right correction plane. Thus, the voltage appearing on the arm 173 is B1b and the voltag on arm 174 is -B2b.

With the left-hand arms of the transfer switches 150 and 151 in the position shown, itwill be observed that the voltage-A1` on the line-141 appears across the resistorfs153"and`154, the voltage ',-Agon v'the line Y'143 fappearsacross 4therresistnors 156 and 160,-thevoltagejl-B1 4on the line 145 appears across the resistorsj1'62 and'1`63, andthe voltage -l-B2 on the line 147 appears across the resistors 165 andV 16,67.v The purpose ofthese resistors isrto maintain the output Yimpedance onthe potentiome- ,ters 117 118, 119 Aand 120V substantially constant Vas between the operational positions of the switches; p Y Before proceeding, the Aeffect of actuating the transfer switches 150 and 151 for operating with a Y-type -'article Vwill be mentioned. f o Y' Q With the" right-hand movable arms of the transfer switches in the position shown bythe dotted lines, vit will be apparent that the voltage -Al' on line 141isacross the'potentiometer7155, the voltage 'Ag on line 143 is across the'potentiometer 161, the voltage -l-Bl online 145 is across theY potentiometer V164, and thevoltage f-l-Bz on Vthe `line`147 is across the` potentiometer 170. Therefore, thevoltage onV arm 171 is V Alfa thef'voltage on ari-n 172 is --A2a,the` voltage on arm 173 is -l-pB'lb, and the voltage on arrn 174 isrY-l-Bzb.- i Inl view'oflthe above,V it will beobserved'tha't, depending on theVV position of the switches"150 and V151, the 'line`s117'5 176, 180 and 181 connected to arms 171,172, 173 and 174 will alternatively have the'voltagesras indicated. Y f' In Pconnectionjvith keepingfthe output impedance of the potentiometers117,118, 119 and 128 constann'the following shouldibe noted.Y vThe dotted`line positionfjof the right side arms of switches 150and'151 throws re# sistances'lS,,156,1621and 1165 across'thepotentiometers Y as .interconnected by the lines 141, 143, YV145 and 147. Also, theVK dotted'lin'e Yposition` lof' the left-bandi arms ''throws resistarics 154,V 1160, 163i and`166 across ythe potentiometers as linterconnected by the lines 140,142, 144V and146. Preferably the resistances 153A, 154,155, 156, 160, *161, 162, 163, 164, 165, 166 and 170 are 0f Ysubstantially equalevalue. C Y o Y l Returning nowfto 'operation of the Vsystem(.witlttffthe transfer kswitch set'for operation with an'X-typ'elarticle:

VThe *left `and V'right' plane switchu 182 sets up the systern for multiplying certainofthehorizontaland'vvei'tical components of the measurement. planes by the distance c separating the correction planes as'required byY the opera-V tional equations. The details of construction off this switch and its operation follow.

The Vswitch has an upper portion 18211 and alower: portionV 1821. InV the upperV portion, the upper terminals Y for operation in the rightV plane. 'Asindicatedthe movable armsrare ganged for simultaneous operation. The potentiometers '184 and186 are multipliersile.; there'sistances of the potentiometers are arranged Vso that whenthe movable arms 19il`1and 131 are set in'accordance with the 'distance Vbetween correctin'planes,"rthe vo1tage"`,o'n anarm is equal to the voltage across'the resistances times thef distance c. c'

Thus, when thefswitch 182 is set forY theleftv plane, the voltage -1-A Vappears across the'potentiometer 184 and Ythe voltage on the movable arm 190 is +A1c and the volt# age +A2 'appears across' the potentiometer 186 and the voltage on the arm 191 is" -lV-Ac. When the switch 'is set for the right'plane, Vthe voltage -Bl appears on the potentiometer' 184 and the voltage .on the arm190 -is #Bic and the voltageY .B appears on the potentiometer 186 and the voltage on the arm 191is Bez In summary" then, the lines 192 and 193 connected' to the arms 190'and 191 carry, depending on the position Yo` switch 182, voltage +A1c'or -Bic and i--i-'Azc or 'Bgc as is indicated. f Y r e The `next operation is to algebraically sum the voltages or products `mentioned above. VThis is preferably done by horizontal and vertical summing amplifiers/,generally designated by l`94and 195. Y Y These summing/amplifiers are preferably'highfgain amplifiers 'with aV feedbacltloop, the' `operationof which isY wellfunderstood in`the`art and need' not be described .indetailg The following shouliisuilce` for present'purposes. YThe input toA the :horizontal amplifier is from lines 181D, 175 and 192. The outputv of this Vamplifier is designated as 200 andthe/feedback circuit generally'indicated'at 201. rIn Vthe vertical summing ampliier, :the inputis from lines 193, 176`and 181. Theroutput `,0f the ampliier is designated by 202 and the feedbachicircuit generally lindicated at Y203. Y

i' With the plane s'witch'182 inthe position fortherleft N plane, the input .toY theY horizontal amplitier is ,-Blb,

Yfl-Altz, i-Alc, while V,theV input to the vertical amplier is '-Bgbgi }`A2a,1 -l-Ago; `Byi an inspection of operating Equations 3a. and 3b; it will Vbe seen` that the aboverinputs are the same as the numeratorio these equations.Y

-are connected toV line 140 carrying'volta'ge -l-A1, while Y the lower terminals are connected to Vline 144 carrying the voltage YB1. The left-hand movable arm connects a Vresistor' 183 to the upper vor lower terminals, depending uponwhether it is in the; positionV as shown lorcin the dotted line position.V The right-hand movablejarm Vcon-A nects a potentiometer 184 lto the upper vor lower terminals,

thedottedvline position. r 'Y g o' dependingon whether it is in the positionY as shown or in In the lower p'ortiomthe upper terminals are connected itotline 142 carrying voltage +A2, while'th'e lower Jtelminals are connected to the" line 146carryingvoltge -B2. The left-hand movable ann 'connects aresist'or Y 185' tofthe'upper gorl lower terminals, depending Yupon whetherit is in the position shown'o'r in the dotted Vline position.v vThe right-hand movable armrconnects a'potenfA l `tiorneter186 to `the uppermor lower terminals, depending 'upon whether itis in the position/shoifrrtor` in/ the dottedVY YVYV1ine.position. n N Y v, Y The resistors Y.183 and185. are. used in conjunction l with the yresistors'153s,- ett:., oftransfer switches 150 and .V151 for maintainingqproper- `impedance acrossthefpotentiorneters'V 117, etc;r

""Therposr 'ons-of the Irun/ablev arms of the plane-switch Y Y winding 214Y feeds a- -B1b, `-B1c, while the inputto the vertical amplifier is +A2a,'-Bb,; -Bza Vv)By an inspection of the Yoperating Equations 3c and 3d,1`it will be seen that the above inputs are the Same as the numerators of these equations except for signs. The change in signY of the inputs from that required by the operating equations Vis compensated for by the switch 204 ganged-to the plane switch 182. When the plane switch is set for the left plane as shown, the

n yswitch 204 feeds theevoltage romthe power supply through line 205 'to the reference phase 296 of a servo motor QM, However, when'the Vswitch 204`is setfor right plane operation, the switch 204 is actuated and the voltage feed, to the reference Vphaser2i6 is of they opposite instantaneous polarity or 1805'` out of phase. This phase Vshift compensates for the sign change of the inputs in the operation o'fa component solver generally vdesignated by 210 asY will' be observedhereinafter.

The purpose of the component solver 218 `is to nd the vector sunroof theoutputs ofthe summing amplifiers and to indicate Ythe angle or orientation `of the resultant from the referenceor horizontal'plane mentionedv heretofore. The solver has two statorKV windings 211and 212 respectively connectedto the output iines Ziliand 2020i the horizontal andvertical summing amplifiers. These Ywindings are in` 90.` 1 Yspace quadrature'.` Two rotor windings 213 and 214 are oriented at 9i)" torone another, the

winding 213 being connected to servoamplier215eeding the controlcoil 2.16A of the servo, motoreM.TheT

ividing 1 circuit 217 th purpose of? f o o M laindblow 'Ih se connected to the rotor windings 213 and 214 and rotates the same.

The outputs of the summing amplifiers fed to the component solver are in phase inasmuch as there is no phase Y shifting in the system as between the transformer secondaries 110--111 and the summing amplifier outputs. Also, these voltages will be in or out of phase with the phase of the voltage across servo motor coil 206, depending on the position of the switch 204. The magnitudes of the outputs of the vertical and horizontal amplifiers usually will differ, depending on the values of unbalance.

The component solver 210 may be a standard com' =taanI -e-zl-zl e211 This angle then is the angle of unbalance (a or in the left or right correction planes, depending on the position of switch 182. Also, with reference to Equations 3a, 3b, 4a and 4b, it will be noted that the complete solution requires a division operation by c, the distance between correction planes. In other words, the voltage appearing across the coils 214 is the vector sum of the stator inputs but does not representy the I' or (the vectors in the correction planes) until divided by c. This is done by the circuit 217.

This circuit may be of standard design comprising an amplifier 220, input resistor 221, output potentiometer 222 and feedback loop including resistor 223. The circuit is arranged so that when the movable arm 224 is set in accordance with the distance c between correction planes, the output voltage is reduced or divided by this factor. The meter 225 connects to the output of the dividing circuit, then indicates the amount of unbalance in the left or right planes, depending on the position of switch 182. Preferably the arm 224 is ganged to the arms 190 and 191 as indicated.

When a Y-type article is to be tested, the operation of the device is the same as above described. However, the switches 182 and 186 are actuated as mentioned heretofore so that the proper voltage will be fed to the horizontal and vertical summing amplifiers. Also, the various distances a1, b1 and c are set up as required. No further explanationneed be given for the operation, as this will be apparent from a comparison of operating Equations 7a-7d with the circuitry of Figure 4.

Another embodiment of the invention is shown in Figure 5. This apparatus is for use particularly with operating Equations 4rz-4d. A brief explanation follows.

The embodiment shown in Figure 5 is arranged somewhat diticrently than that described in connection with Figure 4, particularly in the sense that the determination of unbalance Vin each of the correction planes is accomplished simultaneously rather than switching from plane to plane (by switch 182). Other differences will be noted as the description proceeds.

The potentiometers 230 and 231 are adapted to be supplied with constant A C. voltages by a power supply similar to that mentioned in connection `with Figure 4, and operate in a similar manner. The arm 232 of potentiometer 230 and the arm 233 of potentiometer 231 are respectively adjusted in accordance with the amount of unbalance in the left and right measurement planes. output voltages A and B are fed through isolating transf formers 234 and 235 to potentiometers generally designated by 240 and 241, which resolve the input voltage into horizontal and vertical components similarly as described in connection with the potentiometers 117, etc. The potentiometer 240 is operated'in accordance with the angle 0, while the potentiometer 241 is operated in accordance with the angle. qb.

As indicated, the output lines of the potentiometers 240 and 241 carry voltages -l-A1, etc., and -l-B1, etc.,I which are fed to isolating amplifiersV 242, 243, 244, 245, 246, 247, 248 and 249. The purpose of these amplifiers is to maintain the output impedance of the potentiometers 240 and 241 substantially constant. The output lines Z-257 of the amplifiers 242--249 carry voltages |A1, etc., and }B1, etc.

These output lines are connected to a group of summing and dividing networks generally designated by 260-263. These networks are similar in form and explanation will be made only in connection with unit 260. This comprises resistors 264, 265 and 266 connected to the lines 250, 254 and 251, which make up the input to an amplifier 270 having a feedback loop including resistor 271. The general equation for such a network is E0=Rf[E1/R1+E2/R2+ E11/Rn] Where E0 iS the output voltage, E1, E2, etc., are input voltages, R1 is the feedback resistor and R1, R2, etc., are the input resistances. By making R1=1/c, E1, E2, etc., the appropriate horizontal and vertical components and R1, R2, etc., the reciprocal of the appropriate distances a, b, c, d, the operating Equations 7a-7d can be solved.

Thus, in network 260, the input resistors 264 and 265 are proportional to 1/ b, the input resistor 266 is proportional to l/d, andthe feedback resistor 270 is propor tional to l/c. Also, it will be noted that the lines 250, 254' and 251 carry voltages -l-A1, {B1 and '-A1. By substituting these in the general equation:

which, it will be noted, is the same as Equation 4a except for the -sign. The line 272, which is the output line of amplifier 270 carries voltage -K1. The output lines 273, 274 and 275 carry voltages -K2, -L1 and L2.

In the amplifiers 280, 281 and 282 for the networks 261, 262 and 263, the feedback resistances are proportional to l/c, as is indicated, and the respective input resistances are proportional to the required l/b, l/a and lld factors as is also indicated. Also, these input resistors are interconnected as shown to the amplifiers 244-249 to receive the proper component voltages therefrom.

The voltages K1 and K2 on lines 272 and 273 are fed to the left correction plane component solver 283, while the voltages L1 and L2 on planes 274 and 275 are fed to the right correction plane component solverk 284. These component solvers operate in a manner as described in connection with the solver 210 of Figure 4. The amount of unbalance K in the left correction plane is indicated by the meter 285, while the angle a is indicated by the position of the solver rotor or by the servo M1. The amount of unbalance L in the right correction plane is indicated by the meter 290, while the angle ,B is indicated by the position of the solver rotor or bythe servo M2.

We claim: i

1. In a balancing machine having means for determining for each of two measurement planes of an article the amount and the angle of unbalance with respect to a K sum thereof.

reference plane, a computer for YVdeterminingthe, amount Yand angle of unbalance `in tworcor'responding correction f planes comprising: meansito develop voltages Vrepresenting l respectively the amount of unb'alanc'einV said measurement Y'planes means receivingsaid voltagesrand operativeV asia function of theV respective angles of unbalance of said urement planes voltages representing; 90- `components of unbalance; mechanism foreach correctionV plane for determining the value of the `90"r components( ofrzeach measurement plane inthe corresponding'rcorrje'ction,planes and developing 4voltages in accordance" therewithg: t and means selectively Vresponsiveto, the Vvoltages ofjsaid mechanism Vto determine Y. respectivelyl for each correction g Y plane the magnitude'andangle ofthe vector sum Vof the Y voltagesrrepresenting the-90"V components'oi-unbalance Y therein. y Y

w 2. In a balancing machine having meansto determineV for a measurement "plane of. an article 'the' amount and the angle of imbalance with respect'to a reference plane, a computer for determiningf the anglefrand amount of unbalance ina'correction planey comprising: means tofdevelep for saidplane arvoltage representing the amount of unbalance; electrical circuit meansreceiving said voltage to develop voltagesY correspondingv to lthe 90 com- Y 'ponents 'of unbalance insaid measurement-.planeameans Y' responsivev to lastj said voltages to develop voltages proportional'to the value ofthe 90components of imbalance in a plane of correction spaced from saidplaneof measurement; andme'ans to obtain the amount. and angle of imbalance for Asaidfcorrection plane including', mechanismA Y' Vto vectorially'add lastgsaid voltages. Y .c

3.'In a balancing machine having means to determine Y vfor left and rightl measurement planes of an article the amount and the angle of unbalance with respect to a refer- Vence plane; arcomputer' for determiningther-amount` and angle of unbalance in a left and right measurement plane;

'the combination comprising: means to developY voltages Y representing respectively the amount of unbalance in said left and right measurementvplanes means receiving said voltages and operative as a function of the respective angles of unbalance in said measurement planes to de- 4 .4@ In a balancing-machine having means for determining forY eachr of two measurement lplanes of an'- article-*the amount and the angle of unbalancegwithrespect to a reference plane, a computer for determining the amount and angleV of unbalancegin two correction planes comprisingi means to develop voltages representing respec- 'tivelyV the amount of-'unbalance nint eachfsaid measurement plane means yreceiving 'said' voltages and operative as a function of the respective angles of unbalance of vsaid Y vmeastuementA planes tor-develop Iespectivelyjfor said measurement planes voltages representing the 90?components. oiunhalance; mechanism V.for eachcorrection planek for determining the value'of.the.90V components of each measurement plane in the corresponding correction planes anddeveloping voltages in accordance therewith; means responsive to'last said voltages and operative for each correction plane for determining the vector surn of the voltages representing the 90 components of unbalance therein;V and means koperative for each correct-ion plane. for indicating `the magnitude-and angle of therespective vector sums.

'1 .1 5,. In 1abalancing machine having means L for determim. ing for left and right-measurement planes of an article theA amount LandfangIeV of unbalancewith respect-*to` a reference planei''af-cornputerior determining the amount- 5. and angle ofunbalance in two correction-planes comprismeasurement'planes 'todevelop respectively for said meas-1 ing :i means to -V develop voltages representing respectively the amount ofrunbalance in said left-andright measurement; planes' means receiving-said voltages and operative as'afunction ofthe respective angles ofunbalance of-said l() left and'Y right measurement planes to'develop respectively for-said measurement planes voltages #representing -the 90?; components of'unbala'nce; first mechanism for deterl miningthevalue'of the-90 components'ofpthe leftmeasurementV plane in thev left correction planeand develop- 15 ing voltages in 'accordance therewith; second mechanismfor'deter'r'nining the value of the-'90 vcomponents ofVVV the Y right measurement plane in theright correctionplane and developing voltages'in accordance therewith; means responsive to the-voltages of saidy rstmechanism to determineithemagm'tude and angle off the vectorisum thereof;

and means responsive*V to j the *voltages of said second mechanism to determine the magnitude and angle of the vector sum thereof. Y

Y Y 6. In a balancingA machine .having means for determining for each of two measurement planes of an article the amountV and angle 'of unbalance with respect toa reference plane, a computer for determining the amount and angle of unbalance Vin two correction planes comprising:

means to independently develop foreach said measure- O mentplane, a voltage representing Ythe amount of unbalance of .the articlesymeans to develop respectively from said measurement voltages, voltages-representing the 90 components of unbalance; mechanism for each correction plane effective to.,multiplyK-thevoltage representing one 5 component 'ofl each measurement plane Yrespectively by quantities reprcsentingrthe lrespective distances to the correction plane Vwherein values arenot being determined and 'effective to `multiplynhe voltage representing the other component-'of each measurement plane, Vrespectively by O quantitiesrepresentingtherespective distances to the correctionplane wherein values are not being determined;

Y means operative `for;both correction planes; toreceive Y the multipliedV said one Vcomponent voltages and to algebra- Y ically sum the same andn develop .an outputUvolt-age in accordancewithrthe sumand to receive the multiplied said other component voltagesland algebraically sum the same and develop Yanoutput voltage in'accordance with the sum; Y means connected to. 'receivesaid output/voltages and develop an Youtput signal proportional kto the vector-)sum 59 thereof includingV means toindicate the arc-tangentY of the ratio of the outputs; means to receive last said signal-and Y divide Vthe same by a vquantity representingthe distance between correction planes; and'mechanism to. indicate last 'said quotient. Y Y Y -V j Y 7. In a balancing machine having means for .determining forv left and right measurement planes of an article the amountand angle of unbalance with respect to a reference plane,a computer for determining the amount and angle of unbalancerin t-wocorrection *planes comprising: means to @D develop `a voltage-representing the .magnitudes of unbalanceiu said left measurement; plane; means toY develop Va voltage representing the magnitudetof `imbalance yinfsaid Yrighhmeasurement plane;V means .to multiply said magnitude voltage of theleft measurement-planeby the-sine .55 and cosine of the angle of unbalance in the left measurement plane rand develop Voutput-'voltages in. accordance therewith-last said outputvoltagesrepresenting com- .ponents of unbalance; means to multiplyr said magnitude voltage ofY the rightmeasurement plane by the sine and 79 cosineof thefangle ,of unbalance of the, right-,correction planeand develop outpntvoltages in accordance therewith, last said output voltages representing 90.components of unbalance; mechanism fordetermining the yvalne of Athe cosine -componentofV-the left measurement Yplane in the 75 -left correction plane including means .to-*multiply the co- 13 sine component of the right measurement plane by its distance to the right correction plane, to multiply the cosine component of the left measurement plane by its distance from the left correction plane and bythe distance between correction planes and thereby develop three left cosine voltages; mechanism for determining the value .of the sine` component of the left measurement plane in the 'left correction plane including means to multiply the sine component in the right measurement plane by its distance to the right correction plane, to multiply the sine component in the left measurement plane by its distance from the left correction plane and by the distance between correction planes and thereby develop three left sine voltages; mechanism for determining the value of the cosine component of the right measurement plane in the right correction plane including means to multiply the cosine component in the left measurement plane by its distance to the left correction plane, to multiply the cosine component in the right measurement plane by its distance from the right correction plane and by the dist-ance between correction planes and thereby develop three right cosine voltages; mechanism for determining the value of the sine component of the right measurement plane in the right correction plane including means to multiply the sine component in the left measurement plane by its distance to the left correction plane, to multiply the sine component in the right measurement plane by its distance from the right correction plane and by the distance between correction planes and thereby develop three -right sine voltages; first summing means to sum a plurality of voltages fed thereto and develop an output voltage in accordance therewith; second summing means 'adapted to sum a plurality of voltages fed thereto and develop an output voltage in accordance therewith; mechanism alternatively 14 operable to feed said three left cosine voltages to said rst summing means and said three left sine voltages to said second summing means or to feed said three right cosine voltages to said rst summing means and said three right sine voltages to said second summing means;

mechanism connected to said summing means to receive the respective output voltages therefrom and to develop an output signal proportional to the vector sum of the outputs including means to indicate the arc-tangent of the ratio of the outputs; means to receive last said output signals and divide the same by a quantity representing distance between correction planes; and means to indicate last said quotient.

References Cited in the le of this patent UNITED STATES PATENTS OTHER REFERENCES Pages 52-5 6, Elements of Mechanical Vibration by Freberg and Kemler. Published 1947 by Wiley. 

